Probabilistic Models of Dynamic Response and Bootstrap-Based Estimates of Extremes: The Routines MAXFITS

This report describes and illustrates the use of the routine MAXFITS. This routine estimates statistics of extremes corresponding to arbitrary dynamic load or response processes. It estimates statistics of extremes from limited duration time histories, which may arise either from experimental tests or computationally expensive simulation. A wide range of statistics-e.g., mean, standard deviation, and arbitrary fractiles-can be estimated for an extreme over an arbitrary duration T. The routine also assesses, through boot-strapping methods, the statistical uncertainty associated with these extremal statistics due to the amount of data at hand. This will consistently reflect the growing uncertainty as, for example, we extrapolate to (1) increasingly high fractiles of the extreme response; or (2) increasingly long target durations T, relative to he length of the input signal.

Central to this routine is a core group of algorithms used to probabilistically model various aspects of the dynamic process of interest. The user is permitted to model either the time history itself, a set of local peaks (maxima), or a coarser set of global peaks (e.g., 5- or 10-minute maxima). A number of distribution types are included for these various purposes. For example, normal distributions and their 4-moment transformations ("Hermite") are included as likely candidates to apply directly to the process itself. Weibull models and their 3-moment distortions ("Quad ratic WeibuII") have been found particularly useful in modelling local peaks and ranges. Extremal, Gumbel models are also included to permit natural choices of global peaks, These algorithms build on the distribution library of the FITS routine documented in RMS Report 31 (Kashef and Winterste in, 1998).

To focus on upper tails of interest, the user can also supply an arbitrary lower-bound threshold, ælow , above which a shifted version of a positive random variable model-exponential, WeibuIl, or quadratic Weibull-is fit. In estimating the annual maximum response, the program automatically adjusts for the decreasing rate of response events as the threshold ælow is raised.

This program is intended to be applicable to general cases of dynamic response. A particular example shown here concerns the extreme offset statisitics of a floating spar buoy offshore structure. This parallels the ongoing floating structure research carried out by the Offshore Techonology Research Center, who has adopted the spar as a "theme structure" for both experimentaland analytical study.